Fast Update of Conditional Simulation Ensembles
Clément Chevalier, Xavier Emery & David Ginsbourger
Résumé |
Gaussian random field (GRF) conditional simulation is a key
ingredient in many spatial statistics problems for computing
Monte-Carlo estimators and quantifying uncertainties on non-linear
functionals of GRFs conditional on data. Conditional simulations
are known to often be computer intensive, especially when appealing
to matrix decomposition approaches with a large number of simulation
points. This work studies settings where conditioning observations
are assimilated batch sequentially, with one point or a batch of
points at each stage. Assuming that conditional simulations have
been performed at a previous stage, the goal is to take advantage
of already available sample paths and by-products to produce
updated conditional simulations at minimal cost. Explicit formulae
are provided, which allow updating an ensemble of sample paths
conditioned on n≥0 observations to an ensemble conditioned on
n+q observations, for arbitrary q≥1. Compared to direct
approaches, the proposed formulae prove to substantially reduce
computational complexity. Moreover, these formulae explicitly
exhibit how the q new observations are updating the old sample
paths. Detailed complexity calculations highlighting the benefits
of this approach with respect to state-of-the-art algorithms are
provided and are complemented by numerical experiments. |
Mots-clés |
Gaussian random fields Residual kriging algorithm Batch-sequential strategies Kriging update equations |
Citation | Chevalier, C., Emery, X., & Ginsbourger, D. (2015). Fast Update of Conditional Simulation Ensembles. Mathematical Geosciences, 47(7), 771-789. |
Type | Article de périodique (Anglais) |
Date de publication | 2015 |
Nom du périodique | Mathematical Geosciences |
Volume | 47 |
Numéro | 7 |
Pages | 771-789 |
URL | http://link.springer.com/article/10.1007/s11004-014-9573-7 |